Solve for $x$ and $y$ using elimination. ${-x-5y = -37}$ ${x-6y = -29}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. $-11y = -66$ $\dfrac{-11y}{{-11}} = \dfrac{-66}{{-11}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {-x-5y = -37}\thinspace$ to find $x$ ${-x - 5}{(6)}{= -37}$ $-x-30 = -37$ $-x-30{+30} = -37{+30}$ $-x = -7$ $\dfrac{-x}{{-1}} = \dfrac{-7}{{-1}}$ ${x = 7}$ You can also plug ${y = 6}$ into $\thinspace {x-6y = -29}\thinspace$ and get the same answer for $x$ : ${x - 6}{(6)}{= -29}$ ${x = 7}$